Public Goods 2

# Public Goods 2 - Variable Public Good Quantities E.g. how...

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Variable Public Good Quantities E.g. how many broadcast TV programs, or how much land to include into a national park.

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Variable Public Good Quantities E.g. how many broadcast TV programs, or how much land to include into a national park. c(G) is the production cost of G units of public good. Two individuals, A and B. • Private consumptions are x A , x B .
Variable Public Good Quantities Budget allocations must satisfy x x c G w w A B A B + + = + ( ) .

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Variable Public Good Quantities Budget allocations must satisfy MRS A B are A & B’s marg. rates of substitution between the private and public goods. Pareto efficiency condition for public good supply is x x c G w w A B A B + + = + ( ) . MRS MRS MC A B + = ( ). G
Variable Public Good Quantities Pareto efficiency condition for public good supply is Why? MRS MRS MC A B + = ( ). G

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Variable Public Good Quantities Pareto efficiency condition for public good supply is Why? The public good is nonrival in consumption, so 1 extra unit of public good is fully consumed by both A and B. MRS MRS MC A B + = ( ). G
Variable Public Good Quantities Suppose • MRS A is A’s utility-preserving compensation in private good units for a one-unit reduction in public good. Similarly for B. MRS MRS MC A B + < ( ). G

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Variable Public Good Quantities is the total payment to A & B of private good that preserves both utilities if G is lowered by 1 unit. MRS MRS A B +
Variable Public Good Quantities is the total payment to A & B of private good that preserves both utilities if G is lowered by 1 unit. Since , making 1 less public good unit releases more private good than the compensation payment requires Pareto-improvement from reduced G. MRS MRS MC A B + < ( ) G MRS MRS A B +

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Variable Public Good Quantities Now suppose MRS MRS MC A B + ( ). G
Variable Public Good Quantities Now suppose is the total payment by A & B of private good that preserves both utilities if G is raised by 1 unit. MRS MRS MC A B + ( ). G MRS MRS A B +

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Now suppose is the total payment by A & B of private good that preserves both utilities if G is raised by 1 unit. This payment provides more than 1 more
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## This note was uploaded on 12/26/2011 for the course ECON 100B taught by Professor Kilenthong during the Fall '08 term at UCSB.

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Public Goods 2 - Variable Public Good Quantities E.g. how...

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